Method and apparatus for multiple antenna communications, and related systems and computer program

ABSTRACT

A method of detecting sequences of multi-level encoded symbols. The multi-level encoded symbols are mapped and modulated with a modulation scheme having a number of constellation points identified by a sequence of bits arranged in at least a first and a second group. The first group is encoded with a first encoding scheme, and the second group is encoded with a second coding scheme, and the multi-level encoded symbols are transmitted by multiple transmitting sources and received as a received vector by multiple receiving elements. 
     A first set of candidate sequences is selected and a first set of probability information is calculated for the first set of candidate sequences. Then the first group of bits of the symbols are decoded. The decoded bits of the first group are re-encoded and used to select a sub-set of constellation points. 
     A second set of candidate sequences is selected based on this sub-set of constellation points and a second set of probability information is calculated for the second set of candidate sequences. Finally, the second group of bits of the symbols are decoded.

TECHNICAL FIELD

An embodiment of the present disclosure relates to communicationtechnology.

Specifically, an embodiment of the disclosure concerns a multi-levelcoded modulation arrangement applied to a spatial multiplexingMultiple-Input Multiple-Output (MIMO) Orthogonal Frequency DivisionMultiplexing (OFDM) systems.

BACKGROUND

Throughout this description various publications are cited asrepresentative of related art. For the sake of simplicity, thesedocuments will be referred by reference numbers enclosed in squarebrackets, e.g. [x]. A complete list of these publications orderedaccording to the reference numbers is reproduced in the section entitled“List of references” at the end of the description. These publicationsare incorporated herein by reference.

Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency DivisionMultiplexing (OFDM) systems are promising solutions for next generationWireless Local Area Network (WLAN) system thanks to the high data rateachievable. The OFDM technique is a promising method for high data ratecommunication systems due to its simple implementation via FFT androbustness against frequency selective fading channels. In a spatialmultiplexing MIMO system, high data rate transmission is achieved byde-multiplexing the data sequence into N sub-streams that aretransmitted through N antennas. Thus, MIMO-OFDM systems can provide highperformance and reliable transmission.

The introduction of more antennas at the receive side involves aremarkable computation burden related to the extraction of theLog-Likelihood Ratios (LLR) from the received signal. This applies i.a.to the computation of the A-Posteriori Probabilities (APPs), which isvery complex and whose computational complexity increases with p^(N),where p is the number of constellation points.

Therefore, typically only suboptimal techniques are used when p islarge. An example of such a suboptimal technique is disclosed in [1].

Other solutions are based on multilevel coding for multiple-antennasystems. For example, [2] presents a comparison among different schemes.

SUMMARY

An embodiment of the disclosure provides a fully satisfactory responseto the needs outlined in the foregoing. Embodiments of this disclosureprovide an effective low complexity solution for multilevel coding anddecoding for multiple antenna systems.

Embodiments of the disclosure relate to a method, correspondingapparatus, as well as a corresponding related computer program product,loadable in the memory of at least one computer and including softwarecode portions for performing the steps of the method when the product isrun on a computer. As used herein, reference to such a computer programproduct is intended to be equivalent to reference to a computer-readablemedium containing instructions for controlling a computer system tocoordinate the performance of the method. Reference to “at least onecomputer” is evidently intended to highlight the possibility for themethod to be implemented in a distributed/modular fashion among softwareand hardware components.

An embodiment of the arrangement described herein is a method andapparatus to detect sequences of digitally modulated symbols,transmitted by multiple sources (e.g. antennas).

An embodiment of the arrangement described herein is a receiver todetect and decode constellation symbols being encoded with themultilevel scheme.

An embodiment of the arrangement described herein relates to a stagedLLR (e.g. APP) computation and channel decoding arrangement for aMIMO-OFDM system based on a multilevel coding and spatial multiplexing.

In an embodiment, a multilevel receiver is provided having ahierarchical architecture in order to reduce the above mentionedcomplexity.

In an embodiment, a multilevel receiver may perform the following steps:

-   -   computing the LLRs for the first level decoder,    -   decoding the first level code and re-encoding decisions, and    -   selecting sequences of sub-constellations for the second level        detection.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure and its features,reference is now made to the following description of exemplaryembodiments, taken in conjunction with the accompanying drawings.

FIG. 1 illustrates a block diagram of an embodiment of a MIMOcommunication system.

FIG. 2 illustrates a block diagram of an embodiment of a multi-levelMIMO transmitter.

FIG. 3 illustrates an embodiment of an 8PAM mapping.

FIG. 4 illustrates a block diagram of an embodiment of a multi-levelMIMO receiver.

FIG. 5 is a block diagram showing an embodiment of how candidatesequences may be selected.

DETAILED DESCRIPTION

FIGS. 1 through 5 and the various embodiments described in thisdisclosure are by way of illustration only and should not be construedin any way to limit the scope of the disclosure. Those skilled in theart will recognize that the various embodiments described in thisdisclosure may easily be modified and that such modifications fallwithin the scope of this disclosure.

FIG. 1 illustrates an exemplary MIMO system having N transmitting and Mreceiving antennas which may be used to transmit OFDM signal with Ssub-carriers.

As shown in FIG. 1, such a MIMO system typically includes a MIMOtransmitter 10 and a MIMO receiver 30, wherein the MIMO transmitter 10is coupled to multiple transmit antennas 20 (denoted T₁ to T_(N)), andthe MIMO receiver 30 is coupled to multiple receive antennas 22 (denotedR₁ to R_(M)).

As well known to those skilled in the art, such a MIMO system receivesan input bit stream IB, which is encoded by an encoder 12 andde-multiplexed by a demultiplexer 16 to one of several transmissionchains 18 (denoted T_(x1) to T_(XN)), each transmission chain 18 beingcoupled to one of the transmit antennas 20. Instead of a single encoder12, each transmission chain 18 may have its own encoder operatingindependently from the other transmission chains 18.

Similarly, a MIMO receiver may comprise several receiving chains 34(denoted R_(z1) to R_(xM)) coupled to the receive antennas 22. In anembodiment, each receive antenna 22 receives signals from all of thetransmit antennas 20. In an embodiment, the MIMO receiver 30 comprisesalso a signal processing unit 32 to detect and decode the symbols inorder to reconstruct the original data stream, which may then beprovided as output data stream OB.

In an embodiment, the global average radiated power of the OFDM signalis fixed to S and is independent of the total number of transmittingantennas.

As well known to those skilled in the art, the communication channel fora MIMO system having N transmit antennas and M receive antennas may bemodeled, for each sub-carrier, as a flat fading channel described by achannel state information matrix H of dimension M×N:r=H·ã+wwhere ã=[ã₁, . . . , ã_(N)]^(r) denotes the vector of transmittedsymbols, each chosen from a set A, r corresponds to the receivedM-dimensional vector, and w is a vector of complex Gaussian randomvariables with zero mean and variance σ_(w) ₂ .

The vector ã may be considered as a point in the A^(N) space, andusually the elements of the channel matrix H have a uniform distributedphase and Rayleigh-distributed magnitude with average power equal to 1.

Moreover, such channel matrix H may be considered as being independentof both ã and w and is typically known at the receive side.

In an embodiment of this disclosure, a multilevel coded modulationscheme is used. FIG. 2 shows an embodiment of a MIMO transmitter with amulti-level encoding scheme, which may be used e.g. for 64QAMconstellation.

FIG. 2 shows an embodiment of a MIMO transmitter 10 with three encodinglevels denoted 13 _(LSB), 13 _(MidSB), and 13 _(MSB), respectively, usedto encode data which is transmitted via two transmit antennas 20.

In an embodiment, natural mapping on each dimension is used. As wellknown to those skilled in the art, a 64QAM constellation may beconsidered as being constructed by two orthogonal 8PAM constellationswhose labeling is shown in FIG. 3. The least significant bit of the 8PAMconstellation may take alternating values on the real axis and theEuclidean distance between two adjacent sub-constellations is relativelysmall.

Multilevel coding may be used to provide a higher code protection forthe least significant bit. In an embodiment of this disclosure, thenumber of bits of the constellation symbols is divided into threeportions denominated in the following as least significant bits (LSB),most significant bits (MSB) and the remaining bits therebetween (MidSB).

In the exemplary embodiment shown, the 6 bits of a 64QAM modulatedsymbol are organized in two LSBs, two MidSBs, and two MSBs.

Accordingly, the MIMO transmitter 10 has three different levels eachbeing composed of an encoder 132, an optional interleaver 134, and ademultiplexer 136.

Input data IB is sent, e.g. by means of a switch SW1, to one of theencoding chains 13 _(LSB), 13 _(MidSB), or 13 _(MSB), where the data isencoded by one of the encoders 132. Subsequently, the encoded data isde-multiplexed by the corresponding demultiplexer 136 to one of twotransmission chains T_(x1) or T_(x2), each being composed of a mapper142, such as a 64QAM mapper, and a modulator 144, such as an OFDMmodulator.

In an embodiment, the encoder 132 of the first level 13 _(LSB) providesthe two LSBs of the 64QAM constellation symbol, which are encoded with ahigher coding rate than the encoders of the other levels.

In an embodiment, two independent encoders may be used as the encoder132 of the first level 13 _(LSB), each providing the least significantbit of an 8PAM constellation symbol.

Once the sequence of LSBs has been successfully decoded at the receiverside, the decoder of the second level bits (MidSB) may operate with ahigher Euclidean distance and therefore the second level bits may have alower code protection.

In an embodiment, the encoder 132 of the second level 13 _(MidSB)provides the two MidSBs of the 64QAM constellation symbol with a lowercoding rate than the encoder 132 of the first level 13 _(LSB).

Finally, the MSBs have the largest Euclidean distance and therefore mayhave the lowest protection or, in particular cases, may even be leftun-coded.

In an embodiment, the encoder 132 of the third level 13 _(MSB) providesthe two MSBs of the 64QAM constellation symbol with the lowest codingrate compared to the encoders of the other levels.

As mentioned in the foregoing, also the higher level encoders may berealized by two independent encoders which provide the respective bitsof two independent 8PAM constellations.

Those skilled in the art will appreciate that the number of groups (i.e.levels of the multilevel encoder) and the number of bits in each groupmay change according to the used modulation scheme. Moreover, the groupsmay not necessarily have the same number of bits.

Those skilled in the art will similarly appreciate that a singleconfigurable encoding chain may be used, wherein the encoding rate ischanged.

FIG. 4 shows an embodiment of a possible MIMO receiver 30, which isbased on the staged decoding. Such a MIMO receiver 30 comprises a signalprocessing unit 32 coupled to the receiving chains R_(x1) and R_(x2).The signal processing unit 32 performs the detection and decoding of thereceived symbols.

In an embodiment, the signal processing unit 32 comprises a hierarchicalarchitecture comprised of three detection and decoding stages 34 _(LSB),34 _(MidSB) and 34 _(MSB) which provide the LSB, MidSB and MSB bits ofthe symbols, respectively. In an embodiment the hierarchicalarchitecture is implemented with a pipeline.

The complexity of LLR computation in a MIMO spatial multiplexing systemdepends on the size of the constellation p and on the number oftransmitting antennas N. For example, a classical APP computation wouldrequire the computation of p^(N) correlations. In the case of 64QAMconstellation and 2 transmitting antennas the computational cost wouldbe 4096 correlations.

An embodiment of this disclosure relates to a reduction of thecomputational complexity by means of a reduction of the number ofcorrelations to be calculated, while maintaining performance comparableto the optimal one.

In an embodiment, not all possible sequences are verified but only asub-set of candidate sequences is verified. In an embodiment, the firststage 34 _(LSB) comprises a block 342 _(LSB), which selects a sub-set ofcandidate sequences and calculates the LLRs for these candidatesequences.

These candidate sequences and/or the LLRs may then be de-interleaved bya deinterleaver 344 _(LSB), and decoded by a decoder 346 _(LSB).Specifically, the decoder 346 _(LSB) of the first level 34 _(LSB) isresponsible for selecting the most suitable LSBs based on the set ofcandidate sequences and/or the LLRs.

In the following, a possible arrangement will be described to select thecandidate sequences for the first level. Those skilled in the art willhowever appreciate that any other arrangement may be used to select suchcandidate sequences.

In an embodiment, a minimum mean square error (MMSE) linear interface322 is used, which provides soft decision statistic for the symbols sentvia the multiple antennas.

Such a MMSE linear interface 322 may use the following error vector:e=ã−â=ã−G·rwhere G is a N×M linear weight matrix.By minimizing the mean square error defined as:MSE=E{∥e∥ ² }=E{∥ã−G·r∥ ²}and in the case of average power radiated from each transmit antenna 20equal to 1/N, the following MMSE weight matrix may be calculated [4]:G _(MMSE)=(H′·H+α·I _(N))⁻¹ ·H′where α=N·σ², I_(N) is an N×N identity matrix and “′” denotes aconjugate transposition.

The soft decision statistics for the symbol sent from i-th antenna maytherefore be calculated as:y _(i) =G _(MMSE,i) ·rwhere G_(MMSE,i) is the i-th row of the matrix G_(MMSE).

These soft decision statistics are then sent to the block 342 _(LSB) inorder to select possible candidate sequences and to calculate LLRs.

FIG. 5 shows an exemplary arrangement to select the candidate sequencesfor the first level.

In an embodiment, the 64 possible constellation symbols of the 64QAMmodulation are divided into four local sub-lists 52 one for each of thefour sub-constellations having the LSB fixed to “00”, “01”, “10”, “11”.Such sub-lists 52 may be interpreted as four independent 16QAMmodulations. The number of sub-lists may depend on the number of bitsidentified as LSBs on the transmitter side and the number of elements ineach sub-list may depend on the used modulation scheme.

For each local sub-list 52 of constellation symbols a local sub-listwith C_(LSB) candidate symbols may be determined, wherein the candidatesymbols are typically the symbols closest (i.e. in terms of Euclideandistance) to the soft decision y_(i). Moreover, block 52 may alsoconsider a-priori or a-posteriori information in order to select thecandidate symbols.

In an embodiment, a local list 54 associated with the i-th transmitantenna is obtained as the union of the four local sub-lists ofcandidate symbols.

In an embodiment, a block 56 then generates a global list L_(Global) ofcandidate sequences having (4·C_(LSB))^(N) elements by combining, e.g.in all possible ways, the candidate symbols of the local lists 54.Duplicate candidate sequences may be removed in order to further reducecomplexity.

A block 58 is then able to calculate the LLRs for the candidatesequences. In an embodiment, a max-log Maximum-A-Posteriori-Probability(MAP) computation is used to calculate the LLRs:

LLR(b_(k)) = m(rb_(k) = 0) − m(rb_(k) = 1) where$m\left( {{{\underset{\_}{r}\left. {b_{k} = 0} \right)} = {\min\limits_{1 \in L_{{Global}^{({b_{k} = 0})}}}{{r - {1 \cdot H}}}^{2}}},{k = 1},2,...\mspace{14mu},{\log_{2}p},{{and}{m\left( {{{\underset{\_}{r}\left. {b_{k} = 1} \right)} = {\min\limits_{1 \in L_{{Global}^{({b_{k} = 1})}}}{{r - {1 \cdot H}}}^{2}}},{k = 1},2,...\mspace{14mu},{\log_{2}p}} \right.}}} \right.$where L_(Global)(b_(k)=0,1) indicates the elements of the global listhaving b_(k)=0,1.

The first level LLRs output by block 342 _(LSB) can then be processed bythe first level channel decoder 346 _(LSB) in order to extract the bitsused to create the LSBs of the symbols.

These bits may be used to select the winner sub-constellations among thefour sub-constellations. Specifically, once the first level is decoded,these bits are re-encoded by an LSB encoder 348 _(LSB) and, whereneeded, re-interleaved by an interleaver 350 _(LSB).

The second level 34 _(MidSB) may operate then on the selectedsub-constellations in a similar manner as the first level 34 _(LSB).

In an embodiment, the 16 possible constellation symbols of the 64QAMmodulation, which have been selected by the first level 34 _(LSB) for aspecific antenna, are divided into four local sub-lists, one for each ofthe four sub-constellations having the MidSB fixed to “00”, “01”, “10”,“11”. Such sub-lists may be interpreted as four independent QPSKmodulations. Again, the number of sub-lists may depend on the number ofbits identified as MidSB bits on the transmitter side and the number ofelements in each sub-list may depend on the modulation scheme used.

Subsequently, the block 342 _(MidSB) is able to generate a global listof candidate sequences for the second level having (4·C_(MidSB))^(N)elements by combining, e.g. in all possible ways, the candidate symbolsof the local lists of the second level and to calculate the LLRs for theMidSB bits of all antennas.

The candidate sequences and/or the LLRs of the second level output byblock 342 _(MidSB) are then optionally de-interleaved by a deinterleaver344 _(MidSB) and processed by the second level channel decoder 346_(MidSB) in order to extract the bits used to create the MidSB of thesymbols.

These bits may be used to select the winner sub-constellations among thefour sub-constellations of the second level. Specifically, once thesecond level is decoded, these bits are re-encoded by a MidSB encoder348 _(MidSB) and, where needed, re-interleaved by an interleaver 350_(MidSB).

Also the third level 34 _(MSB) may operate on the sub-constellationsselected by the second level in a similar manner as the previous levels.

In an embodiment, the four possible constellation symbols of the 64QAMmodulation, which have been selected by the second level for a specificantenna, are divided into four local sub-lists one for each of the foursub-constellations having the MSB fixed to “00”, “01”, “10”, “11”.Again, the number of sub-lists may depend on the number of bitsidentified as MSBs on the transmitter side and the number of elements ineach sub-list may depend on the modulation scheme used.

Subsequently, block 342 _(MSB) is able to generate a global list ofcandidate sequences for the third level having (4·C_(MSB))^(N) elementsby combining, e.g. in all possible ways, the candidate symbols of thelocal lists of the third level and to calculate the LLRs for the MSBbits of all antennas.

The candidate sequences and/or the LLRs of the third level output byblock 342 _(MSB) the are then optionally de-interleaved by adeinterleaver 344 _(MSB) and processed by the third level channeldecoder 346 _(MSB) in order to extract the bits used to create the MSBof the symbols.

The final bit stream OB may then be created by combining e.g. by meansof a switch SW2 the separate bits used for the creation of the LSBs,MidSBs and MSBs of the symbols.

The overall complexity, in term of correlations, of the completedetection algorithm, can be calculated, for a 64QAM constellation havingthree levels, as follows:

(4 ⋅ C_(LSB))^(N) + (4 ⋅ C_(MidSB))^(N) + (4 ⋅ C_(MSB))^(N)${where}:\left\{ \begin{matrix}{1 \leq C_{LSB} \leq 16} \\{1 \leq C_{MidSB} \leq 4} \\{C_{MSB} = 1}\end{matrix} \right.$

By choosing C_(LSB)=C_(MidSB)=C_(MSB)=1 and N=2, the system presents theminimum computational complexity, while the system has the highestcomplexity for C_(LSB)=16, C_(MidSB)=4, C_(MSB)=1.

The arrangement is therefore tunable, because the number of candidatesymbols selected for each level may be chosen according to the desiredperformance requirements and computational power. Such are-configuration may also be performed in real-time in order to takeinto account the current transmission conditions. For example, thenumber of candidate sequences may be increased due to a high error rate.

Consequently, without prejudice to the underlying principles of thedisclosure, the details and the embodiments may vary, even appreciably,with reference to what has been described by way of example only,without departing from the scope of the disclosure.

LIST OF REFERENCES

-   [1] M. Magarini, A. Spalvieri. A suboptimal detection scheme for    MIMO systems with non-binary constellations.-   [2] L. Lampe, R. Schober, R. Fischer. Multilevel coding for    multiple-antenna transmission. IEEE Trans. on Wireless Comms., vol.    3, No. 1, January 2004.-   [3] H. Imai, S. Hirakawa. A new multilevel coding method using    error-correcting codes. IEEE Trans. on Information Theory, vol.    IT-23, No. 3, 1977.-   [4] B. Hassibi, “An efficient square-root algorithm for BLAST”, in    Proc. ICASSP, Istanbul, Turkey, vol. II, pp. 737-740, 5-9 Jun. 2000.

What is claimed is:
 1. A method of detecting sequences of multi-levelencoded symbols, comprising: receiving, by multiple receiving elements,the multi-level encoded symbols that are mapped and modulated with amodulation scheme having a number of constellation points identified bya sequence of bits arranged in at least a first and a second group, thefirst group being encoded with a first encoding scheme and the secondgroup being encoded with a second encoding scheme, and wherein themulti-level encoded symbols are transmitted by multiple transmittingelements, the multiple transmitting and receiving elements jointlydefining a transmission channel modeled by a channel state informationmatrix and the received symbols being grouped as a received vector;calculating a soft decision for each of the receiving elements based onthe received vector and on the channel state information matrix; foreach of the receiving elements, selecting a first set of candidatesequences based upon constellation points of the modulation scheme andthe received symbols, the selecting the first set of candidate sequencesincluding, selecting a local sub-set of constellation points for eachpossible sequence of bits for the first group of bits; selecting a localsub-set of candidate symbols for each sub-set of constellation points;selecting as candidate symbols the constellation points in the sub-setof constellation points based upon the soft decision; and combining thesets of candidate symbols in order to form the first set of candidatesequences.
 2. The method of claim 1 further comprising: calculating afirst set of probability information for the first set of candidatesequences; decoding the first group of bits of the symbols encoded witha first encoding scheme based on the first set of probabilityinformation; re-encoding the decoded first group of bits of the symbols;selecting a sub-set of constellation points based on the re-encodedfirst group of bits; selecting a second set of the candidate sequencesbased on the sub-set of constellation points and the received symbols;calculating a second set of probability information for the second setof candidate sequences; and decoding the second group of bits of thesymbols encoded with a second encoding scheme based on the second set ofprobability information.
 3. The method of claim 2, wherein saidselecting a first set of candidate sequences includes: selecting foreach receiving element a set of candidate symbols, and combining saidsets of candidate symbols in order to form said set of candidatesequences.
 4. The method of claim 3, wherein said selecting for eachreceiving element a set of candidate symbols includes: selecting a localsub-set of constellation points for each possible sequence of bits forsaid first group of bits, selecting a local sub-set of candidate symbolsfor each sub-set of constellation points, and combining said localsub-set of candidate symbols in order to form said set of candidatesequences.
 5. The method of claim 4, wherein said selecting a localsub-set of candidate symbols for each sub-set of constellation pointsincludes selecting as candidate symbols the constellation points in saidsub-set of constellation points having the shortest Euclidean distancefrom said soft decision.
 6. The method of claim 1 wherein said selectinga sub-set of constellation points as a function of said re-encoded firstgroup of bits includes selecting the constellation points of saidmodulation scheme having said first group of bits fixed to saidre-encoded first group of bits.
 7. The method of claim 2, whereincalculating a set of probability information for a set of candidatesequences includes calculating Log-Likelihood Ratios as a function ofa-posteriori bit information for said set of candidate sequences.
 8. Themethod of claim 2, wherein said first group of bits is encoded with ahigher coding rate than said second group of bits.
 9. The method ofclaim 1, wherein said modulation scheme includes a 64QAM mapping. 10.The method of claim 1, wherein said modulation scheme includes an OFDMmodulation.
 11. The device of claim 1, wherein said device has at leastone pipeline for performing said detecting sequences of multi-levelencoded symbols.
 12. The receiver of claim 1, wherein said transmittingsources and said receiving elements are antennas.
 13. A device,comprising: a receiver for receiving symbols mapped with a modulationscheme having a number of constellation points identified by a sequenceof bits, wherein the received symbols are grouped as a received vector;a first selector configured to select a first set of candidate sequencesbased on the constellation points of the modulation scheme and thereceived symbols, wherein the first selector further includes a numberof soft decision logic blocks that is equivalent to a number ofreceiving antennae associated with the device and wherein the firstselector is further configured to, calculate a soft decision, for eachof the receiving antennas, based on the received vector and on a channelstate information matrix modelling a transmission channel; select a setof candidate symbols for each antenna, wherein the first selector isconfigured to, select a local sub-set of constellation points for eachpossible sequence of bits for said first group of bits, select a localsub-set of candidate symbols for each sub-set of constellation points,wherein the first selector is further configured to select as candidatesymbols the constellation points in said sub-set of constellation pointshaving the shortest Euclidean distance from the soft decision, combinesaid local sub-set of candidate symbols in order to form said set ofcandidate sequences, and combine the sets of candidate symbols in orderto form the set of candidate sequences; a first calculator configured tocalculate a first set of probability information for the first set ofcandidate sequences; a first decoder configured to decode the firstgroup of bits of the symbols encoded with a first encoding scheme basedon the first set of probability information; an encoder configured tore-encode the decoded first group of bits of the symbols, a secondselector configured to select a sub-set of constellation points based onthe re-encoded first group of bits, a third selector configured toselect a second set of said candidate sequences based on the sub-set ofconstellation points and the received symbols, a second calculatorconfigured to calculate a second set of probability information for thesecond set of candidate sequences, and a second decoder configured todecode the second group of bits of the symbols encoded with a secondencoding scheme based on the second set of probability information. 14.A non-transitory computer-readable medium having computer-executableinstructions for receiving multi-level encoded symbols mapped with amodulation scheme having a number of constellation points identified bya sequence of bits arranged in at least a first group and a secondgroup, the first group being encoded with a first encoding scheme andthe second group being encoded with a second encoding scheme, andwherein the multi-level encoded symbols are transmitted by multipletransmitting elements and received by multiple receiving elements, themultiple transmitting and receiving elements jointly defining atransmission channel modeled by a channel state information matrix andthe received symbols being grouped as a received vector, wherein thecomputer-executable instructions, when executed on a computer, areoperable for: calculating a soft decision for each of a plurality of thereceiving elements based on the received vector and on the channel stateinformation matrix; for each of the receiving elements, selecting afirst set of candidate sequences as a function of the constellationpoints of the modulation scheme and the received symbols, the selectingthe first set of candidate sequences including, selecting a localsub-set of constellation points for each possible sequence or bits forthe first group of bits; selecting a local sub-set of candidate symbolsfor each sub-set of constellation points; selecting as candidate symbolsthe constellation points in the sub-set of constellation points basedupon the soft decision; and combining the sets of candidate symbols inorder to form the first set of candidate sequences; calculating a firstset of probability information for the first set of candidate sequences,decoding the first group of bits of the symbols encoded with a firstencoding scheme as a function of the first set of probabilityinformation, re-encoding the decoded first group of bits of saidsymbols, selecting a sub-set of constellation points as a function ofthe re-encoded first group of bits, selecting a second set of saidcandidate sequences as a function of the sub-set of constellation pointsand the received symbols, calculating a second set of probabilityinformation for the second set of candidate sequences, and decoding thesecond group of bits of the symbols encoded with a second encodingscheme as a function of the second set of probability information. 15.The device of claim 13, wherein the modulation scheme includes a 64QAMmapping.
 16. The device of claim 13, wherein the modulation schemeincludes an OFDM modulation.
 17. The device of claim 13, wherein thefirst calculator is operable to calculate the first set of probabilityinformation for the first set of candidate sequences based oncalculating Log-Likelihood Ratios as a function of a-posteriori bitinformation for the set of candidate sequences.
 18. The non-transitorycomputer-readable medium of claim 14, wherein the multi-level symbolsare mapped with a QAM modulation scheme.
 19. The non-transitorycomputer-readable medium of claim 18, wherein the QAM modulation schemefurther includes OFDM modulation.